Some known functional trainer exercise machines include an upright frame holding one weight stack or dual weight stacks, with left and right arms extending from the frame and each having an outer end comprising a vertical track carrying a vertically adjustable pulley carriage and having indexing holes for adjusting the carriage height. Left and right handles are secured to the ends of cables extending around the pulleys in the respective pulley carriages and secured to the weight stack or stacks via a cable and pulley linkage. In these prior machines, the pulley carriage and pulleys travel along the vertical track and are secured at a selected height by indexing pins which extend through selected indexing holes for adjusting the pulley height and thus the handle position for different exercises. The carriage, pulleys, and indexing pin are all external and project outward from the track, and adjustment can be awkward for the user. The exposed pulleys are susceptible to damage when the handle is released.